Question

How do you find the equation of line that is tangent to the curve `y = x^3` at x = 1?

Answer 1

y-1= 3(x-1)

Explanation:

At x=1 , y=1, hence equation of tangent is required at the point (1,1).

Slope of any tangent to `y= x^3` would be `dy/dx= 3x^2`. At x=1, Slope would be 3.

Point slope form of the required tangent is y-1= 3(x-1)